Acta Psychologica 202 (2020) 102960

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Acta Psychologica

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A shared code for and Arabic digits revealed by cross-modal priming in sighted Braille readers ⁎ Katarzyna Rączya, , Maria Czarneckaa, Dominika Zarembaa, Kinga Izdebskaa, Małgorzata Paplińskab, Guido Hesselmannc, André Knopsd, Marcin Szweda a Department of Psychology, Jagiellonian University, Krakow, Poland The Maria Grzegorzewska University, Warsaw, Poland Department of General and Biological Psychology, Psychologische Hochschule Berlin, Berlin, Germany Laboratory for the Psychology of Child Development and Education, Université de Paris, LaPsyDÉ, CNRS, -75005 Paris, France

ARTICLE INFO ABSTRACT

Keywords: Quantities can be represented by different formats (.. symbolic or non-symbolic) and conveyed via different Tactile priming modalities (e.g. tactile or visual). Despite different priming curves: V-shape and step-shape for place and sum- Distance effect mation coded representation, respectively, the occurrence of priming effect supports the notion of different Number representation format overlap on the same mental number line. However, little is known about tactile-visual overlap of sym- Sighted Braille readers bolic numerosities i.e. Braille numbers to Arabic digits on the magnitude number representation. Here, in a Tactile Braille digits priming experiment, we tested a unique group of sighted Braille readers to investigate whether tactile Braille digits would activate a place-coding type of mental number representation (V-shape), analogous to other symbolic formats. The primes were either tactile Braille digits presented on a Braille display or number words presented on a computer screen. The targets were visually presented Arabic digits, and subjects performed a naming task. Our results reveal a V-shape priming function for both prime formats: tactile Braille and written words representing numbers, with strongest priming for primes of identical value (e.g. “four” and “4”), and a symmetrical decrease of priming strength for neighboring numbers, which indicates that the observed priming is due to identity priming. We thus argue that the magnitude information is processed according to a shared phonological code, independent of the input modality.

1. Introduction information is processed. These studies provided important insights into cross-modal number processing; however, they used non-symbolic Number processing is a fundamental achievement of the human tactile number coding (number of stimulated fingers; Krause, brain and various non-human animal species (Dehaene, Dehaene- Bekkering, & Lindemann, 2013; Cohen, Naparstek, & Henik, 2014; Lambertz, & Cohen, 1998; Feigenson, Dehaene, & Spelke, 2004). Sixtus, Lindemann, & Fischer, 2018). To our knowledge, number coding Quantities can be represented either symbolically (e.g. Arabic digits, in a symbolic tactile notation – Braille numbers – has not previously words) or non-symbolically (e.g. as collections of dots). There is an been investigated. Similar to letters, Braille numbers are represented by ongoing debate about whether or not these converge on the same a combination of dots that correspond to the first 10 letters of the mental representation (Kadosh & Walsh, 2009 vs. Nieder & Dehaene, Braille , preceded by a number indicator (see Fig. 2C). For 2009). Beyond the different formats, numerical information can be example, the number 6 is represented by the Braille letter ‘F’, preceded conveyed via different modalities (e.g. visual vs. auditory). The ques- by the number indicator. Learning to read Braille numbers consists thus tion to what extent different modalities converge on a common un- of learning new associations for existing Braille letter symbols. derlying mental magnitude representation also remains unresolved Numbers are thought to be represented on a mental number line (Knops, 2017). Especially, little is known about tactile-visual overlap of (MNL) which is spatially organized on a continuum of numerical symbolic numerosities i.e. Braille numbers to Arabic digits on the magnitudes where, for cultures with the left-to-right writing systems, magnitude number representation. smaller numbers are to the left of larger numbers (e.g., Dehaene & A few studies to date have investigated how tactile number Changeux, 1993; Dehaene, Dupoux, & Mehler, 1990; Restle, 1970).

⁎ Corresponding author at: Department of Psychology, Jagiellonian University, ul. Ingardena 6, 30-060 Kraków, Poland. E-mail address: [email protected] (K. Rączy). https://doi.org/10.1016/j.actpsy.2019.102960 Received 29 January 2019; Received in revised form 8 November 2019; Accepted 15 November 2019 Available online 18 December 2019 0001-6918/ © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/). ą . czy, et al. Acta Psychologica 202 (2020) 102960

Previous studies suggest that symbolic number formats are represented numerosities are represented in an abstract format and can be accessed in a place-coding regime (Roggeman, Verguts, & Fias, 2007; Verguts, regardless of the modality or notation. Alternatively, counting up to the Fias, & Stevens, 2005). In place coding, activation peaks at a target respective letter upon the presentation of Braille primes would lead to position on the number line (numerical magnitude is coded by posi- different priming functions: step-like for Braille primes and V-shaped tion), while the neighboring numbers are activated with decreasing for number word primes. strength (Roggeman et al., 2007; Verguts et al., 2005; Verguts & Fias, 2004). A different type of coding, called summation coding, is observed 2. Materials and methods for non-symbolic number notations such as collections of dots (1 = one dot, 2 = two dots, 3 = three dots, and so on). In the summation coding 2.1. Participants regime, all number line entries are activated until the target number is reached (numerical magnitude is coded by the sum of activated en- Twenty female subjects (mean age = 25; age range = 22–32) par- tries). The latter type of coding could be expected if Braille students ticipated in the experiment. All participants were right-handed, identified Braille numbers (e.g. 5) by counting up to the ordinal posi- monolingual with normal or corrected to normal vision. The partici- tion of the corresponding letter (e) in the alphabet (“a, b, c, d, e”). pants were students or college graduates with minimum 3 years of The actual type of coding can be revealed by priming studies. higher education (mean = 5 years; range = 3–12 years). The group was Varying the numerical relation between the prime and target number in recruited from participants of two previous projects that were per- number-naming paradigms produces differing performance patterns, formed in 2016 and 2017 and which included a nine-month Braille- depending on the underlying code that has been activated by the prime reading course. During this Braille course, participants acquired tactile (Koechlin, Naccache, Block, & Dehaene, 1999; Reynvoet, Brysbaert, & recognition of all Braille letters in the Polish alphabet (for details, see Fias, 2002; Roggeman et al., 2007). When the number prime activates a Bola et al., 2016). For the purpose of the current experiment, all par- place-code, naming latencies increase with increasing numerical dis- ticipants attended a 3-week course focused specifically on reading tance between prime and target, which leads to a V-shaped priming Braille numbers. The course, which was designed and carried out by an function. Two scenarios are possible for a V-shaped function. The first experienced Braille teacher that also co-designed the previous course, one is distance-related priming: lowest naming latencies for no differ- took place in May 2018, i.e. either one or two years after the main nine- ence: e.g. “four” to “4”, slightly larger for “five” to “4”, and still larger month course. Since numbers in the Braille alphabet are letter symbols for “six” to “4”). Such priming reflects true semantic access to the from A to preceded by a number indicator (e.g. number two is a letter mental number line. In the second scenario, the V-shaped function, is b preceded by a number indicator), participants needed only a three- driven by identity priming only: lower latencies (priming) only for week course to automatize recognizing Braille numbers. Similarly to the identical numerosity (e.g. “four” to “4”) but no effect of distance (same previous one, the course relied primarily on participants' individual long latencies for “five” to “4”, and “six” to “4”), a “narrower V-shape”. work. At the beginning of the course they were given 20 exercises, each This shape most likely reflects a type of priming that does not have to be printed on a single sheet. They were asked to complete one exercise per semantic, and can be based on phonological access only. When the day, blindfolded, and then to check their results visually. During the prime number activates a summation code, naming latencies are first two weeks of the course, a class was held twice a week, during characterized by a step-like priming function where each numerical which participants were given a subsequent set of Braille exercises, quantity activates all entries up to and including the presented quantity. received detailed and personalized instruction about completing them, For example, upon the presentation of a 4-dot prime, the entries 1, 2, 3, practiced a sample set of exercises in the class and received persona- and 4 are activated, thus leading to a step-wise priming function with lized feedback from the instructor. During the last week of the course enhanced performance for all smaller and equal target numerosities. they met individually with the Braille teacher to resolve any potential In the Triple Code Model (TCM), numerical information is thought issues (e.g. regarding proper Braille reading technique) and practice on to be internally represented by three separate but interacting codes: 1) a the Braille display used in the main experiment. Before and after the verbal number code, activated in linguistically mediated operations like Braille number recognition course, we tested the participants' Braille number naming, counting, and retrieval of arithmetic facts from long- numbers, letters and words recognition and tactile acuity with different term memory; 2) the visual number code that allows recognition of tests that we list below. Our main goal here, was to test the participants' Arabic digits and multi-digit numbers; and 3) an analogue magnitude ability to recognize Braille numbers, however, additionally we tested code that represents numerical quantity information (Dehaene, Spelke, whether we would observe an additional improvement in their general Pinel, Stanescu, & Tsivkin, 1999; Molko et al., 2003) in an approximate Braille reading skills and thus their overall fluency in Braille reading. manner. According to the TCM, a visual number code (Fig. 1) is acti- Despite being right-handed, seven of the 20 subjects read with their left vated during visual recognition of e.g. Arabic numbers. However, if hand. This phenomenon – a preference for reading Braille with the non- Braille numbers and Arabic digits would not share a code, we would dominant hand – is common and well described in the population of have to assume another, i.e. tactile code in the Triple Code Model. blind subjects (e.g. Millar, 1997) and has been also reported in sighted Here, we investigated whether the acquisition of tactile Braille digit Braille readers (Bola et al., 2016). The study was approved by the Ja- reading leads to a place-coding type of mental number activation. Such giellonian University Ethics Committee. A written informed consent an activation could be achieved by two mechanisms: Braille numbers was obtained from all subjects before the experiment. Participants were could be mapped directly on a semantic code i.e. co-activate it (Fig. 1 reimbursed for taking part in the study. path A), or they could be mapped onto a phonological code i.e. co- activate it without automatic activation of a semantic code (Fig. 1 path 2.2. Braille reading speed tests B). Alternatively, if the strategies used by Braille number readers in- volve intermediate steps (e.g. counting up to the corresponding letter), The subjects' Braille reading speed was tested twice: at the begin- the result would be a summation-code type of mental number activa- ning of the course and at the end of it, but before the main priming tion. experiment. To test the subjects' Braille reading speed in both visual We used Braille digits presented in the tactile modality as primes, and tactile modalities, we used four different paper tests. Since there and Arabic digits as targets (Fig. 2). As a control, we used number are no standardized tests measuring tactile or visual Braille reading words as primes, and Arabic digits as targets, both presented visually speed in Polish, we created a tactile Braille reading test of single (e.g. Naccache & Dehaene, 2001; Reynvoet et al., 2002). Our reasoning numbers (consisting of 6 rows of Braille numbers), a tactile Braille was that if we observe the same priming pattern, i.e. a V-shape function reading test of single letters (consisting of 6 rows of single Braille letters for the two types of priming, it would indicate that symbolic in Polish alphabet), a tactile Braille reading test of whole words

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Fig. 1. Processing model. The model includes two different number codes of the prime: Visual Code for number words and Tactile Code for Braille digits. Our question was that if primes (tactile Braille and number words) and targets (Arabic digits) share a code, what is the nature of the activated code? The model thus depicts two alternative paths of processing from the prime through the target up to the response (A) via semantic code or directly to (B) phonological code.

(consisting of 4 rows of 4–6 letter long words, printed in tactile Braille) to the long axis of the finger. Each dome was presented for 1.5 and and a visual Braille reading speed test (consisting of 30 words, 4–6 participants were asked to name verbally the orientation of the rows: letters long, printed in a visual Braille font). either perpendicular or horizontal (two-alternative forced choice paradigm). The experimenter noted down the given answers. 2.3. Visual reading speed test 2.5. Braille number recognition test To test the subjects' visual reading speed we used a test previously designed by Bola et al. (2016), which consists of a 400-word passage For the purpose of the main experiment we tested the participants' from the book “Farsa Panny Heni” by Maria Rodziewiczówna printed ability to recognize Braille numbers on the Braille Display (BraillePen on paper. After reading the text silently, subjects were given a test, 12 Touch, a portable 12-cell Braille display http://www.harpo.com.pl/ printed on paper, consisting of 10 multiple choice questions concerning ), which we then used in the main experiment. In this test, participants the text. The overall time needed to read the text as well as the accuracy were asked to read aloud a Braille number (range = 0–9; number of of the given answers were measured. repetitions = 20 per number) that appeared on the Braille display for a varying amount of time (300 ms, 600 ms or 900 ms). 2.4. Tactile acuity test Following the aforementioned three-week course, the subjects per- formed the priming experiment, the details of which are given below. Additionally, we tested the tactile acuity of participants' index finger on the reading hand using the tactile acuity grating orientation 2.6. Main experiment — stimuli task (Van Boven, Hamilton, Kauffman, Keenan, & Pascual-Leone, 2000). Following Van Boven et al. (2000) a set of eight hemispherical plastic Fig. 2 shows the stimuli used in the main experiment. We used domes with gratings in their surfaces was used to stimulate index fin- numbers from 2 to 6 (following Reynvoet & Brysbaert, 1999; Reynvoet gertip of the reading hand. Grates on domes' surfaces form two parallel et al., 2002; Roggeman et al., 2007). Since the number 1 in Braille is the rows of bars and grooves that can be aligned along or perpendicularly only number consisting of only one dot, to avoid an obvious

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Fig. 2. Experimental paradigm. (A) Tactile Braille digit to Arabic digit priming and (B) number word to Arabic digit priming. (C) Stimuli used in the experiment: primes-tactile Braille digits and visual number words; targets — Arabic digits. Participants were asked to name the target Arabic number dis- played on the computer screen in all trials in all conditions.

correspondence (1 dot — number one), this number was excluded. condition each trial began with the presentation of a fixation cross for Primes were either tactile Braille numbers (i.e. a letter preceded by a 765 ms followed by a 200 ms beep and 16 ms break. The prime was then number indicator — a combination which stands for a number in the presented for 300 ms so that it could be perceptible (see Braille number Braille alphabet) displayed on the Braille display, or visual number recognition test). The prime was followed by a 150 ms break. Finally, words (i.e. “sześć”) displayed on the computer screen. Targets were the target was presented for 200 ms, after which participants named always Arabic digits (range = 3–5; see Fig. 2C). Visual stimuli (number aloud the indicated quantity. Subjects had 1500 ms to respond words and Arabic digits) were presented in white against a black (Fig. 2A). The additional catch trials were introduced to measure the background in courier font with a size comparable to the Braille accuracy of tactile prime recognition. In these trials, after the basic numbers (font size: 36, see Fig. 2A). trial, there was a 150 ms break after the target, and then a question mark appeared for 2000 ms, during which the participants were asked 2.7. Main experiment — apparatus to name the prime. In the number words condition (designed after Roggeman et al., 2007) each trial began with a fixation cross for Stimuli were presented on a 13 in. screen (DELL) and on a Braille 515 ms. Then we presented a mask for 49 ms, followed by the prime Display (BraillePen 12 Touch 12, Harpo, Poznan, Poland, http://www. presented for 83 ms. The mask was then presented for 49 ms and, fi- harpo.com.pl/) using Presentation Software (a stimulus delivery and nally, the target was presented for 182 ms, after which participants experiment control program for neuroscience, Neurobehavioral named aloud the indicated quantity. Subjects had 1500 ms to respond Systems, Berkley, USA, https://www.neurobs.com/). (Fig. 2B). The mask was applied only in the number words condition i.e. before and after the visual prime, due to the occurrence of an after- 2.8. Main experiment — procedure image after visual stimulus presentation, a phenomenon unique for the visual stimuli not the tactile ones. Two experimental conditions were tested. In both conditions, the target was presented visually as an Arabic digit (3, 4 or 5). In the Braille 2.9. Main experiment — data analysis condition, the prime was presented as a Braille digit (in the tactile modality, Fig. 2A), while in the number words condition the prime was To establish a statistical difference in the shapes of the priming presented as a written number word (in the ) re- curves, we first performed a repeated-measures ANOVA with prime presenting a number (in the visual modality, Fig. 2B). For each condi- notation (number words vs. Braille), prime and target value on mean tion, we used 3 targets (3, 4, 5) × 5 primes (2–6) = 15 possible com- RTs. We then performed a repeated-measures ANOVA on mean RTs binations of prime–target values (Fig. 2C), which were presented in a separately for Braille and number words. In all repeated-measures random order. The conditions were presented in blocks. There were two ANOVAs, we tested for violations of sphericity using Mauchly's test. To blocks of each experimental condition (4 blocks in total), counter- test whether the V-shape priming curve was determined by identity balanced between subjects. Each block consisted of 150 trials (10 re- priming or a distance-related priming we ran the analysis in both prime petitions of each of the 15 target-prime combinations). In the tactile notations for the zero distance and its two most neighboring distances condition we presented the participants with 15 additional catch trails (−1 and 1). To keep the same target–prime distance, in all conditions (trial + additional naming of the prime after a “?” occurred to ran- we restricted our analyses to 6 prime-target combinations. To further domly check if the participant was paying attention to the prime and as test for semantic priming, we removed target-prime distance 0 and ran an additional measure of the accuracy in recognizing Braille digits). regression analysis for both prime notations. Nevertheless, following Before the first block of each condition, 65 practice trials were given others (Roggeman et al., 2007) we began with a repeated-measures to familiarize the participants with the procedure. In the Braille ANOVA that included all distances.

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Subsequently, we followed with a regression analysis to establish of the Braille course was to master and automatize tactile Braille the difference in regression coefficients for V-shape and step-like pre- number reading, the results show a significant increase in visual Braille dictors in both prime notations (Braille and number words). The V- reading speed as well. function predictor had a value equal to the absolute value of the target value — prime value. If the prime value was greater or equal to the 3.2. Visual reading speed tests target value, then the step-function predictor had a value equal to −1, and a value equal to +1 in cases in which the prime value was smaller The mean reading speed of the text with full sentences (“Farsa Pani than the target value. Following previous studies (Hesselmann, Darcy, Heni”) was 185 words per minute (WPM) (SEM = 12.83; range: Sterzer, & Knops, 2015; Hesselmann & Knops, 2014; Reynvoet et al., 93–296) which is a standard result for visual reading speed in skilled 2002; Roggeman et al., 2007), we fitted the regression equations with adults (e.g. Bola et al., 2016; Hunziker, 2006). The subjects' visual two predictors which coded for a V-function and a step-function, re- reading speed was not correlated with any of the tests measuring Braille spectively. Additionally, we added the target value and an intercept to reading speed [tactile Braille numbers: r(20) = −0.136, p = .566; the regression, which was run for each participant separately tactile Braille letters: r(20) = −0.252, p = .284; tactile Braille words: r (Hesselmann et al., 2015; Hesselmann & Knops, 2014; Lorch & Myers, (20) = −0.138, p = .563; visual Braille words: r(20) = 0.236, 1990; Roggeman et al., 2007). Below we provide the regression for- p = .317]. mula: = b0+b1(x1) + b2(x2) + b3(x3) 3.3. Tactile acuity test y — dependent variable: reaction times (RTs). b0 — the y-intercept. At the onset of the Braille course, the mean grating orientation b1, b2, b3 — unstandardized B coefficients. threshold for the reading finger was 1.87 mm (SEM = 0.19). By the end x1 — independent variable 1 (V-shape predictor). of the course, it had reached 1.53 mm [(SEM = 0.16), which represents x2 — independent variable 2 (step-shape predictor). a significant improvement (t(19) = 2.805, p = .011]. x3 — independent variable 3 (target predictor). A positive regression coefficient for the V-function predictor means 3.4. Braille number recognition test that larger |prime–value minus target–value| distances lead to higher RTs and in this way this predictor codes for the presence of a V-shape Additionally, we tested participants' ability to recognize Braille and i.e. symmetrical decrease of the activation strength. A positive re- numbers on the digital Braille display. Since minute differences exist gression coefficient for the step-function predictor indicates that the between the “feeling” of reading Braille on paper vs. on a digital dis- shape of the priming curve can be described by a step-function in which play, the objective of this test was to precisely determine the reading prime values larger than or equal to the target value lead to faster RTs. accuracy under conditions identical to those used in the main experi- The coefficient patterns for the V-function and the step-function for ment i.e. Braille numbers recognition on the Braille display. In this test, each prime notation were then compared with a paired t-test. As pre- participants were asked to read aloud a Braille number that appeared viously, we began with the regression including all the target–prime on the Braille display for a given time (300 ms, 600 ms or 900 ms). After distances (−3 up to 3, including zero distance) and followed with the participating in the Braille course, on average participants recognized regression restricted to the two most-neighboring distances. We com- 88% (SEM = 1.79; range = 14–20 numbers out of 20 possible) of pared the pattern of coefficients for the V-function and the step-func- Braille numbers displayed for 900 ms, 77% (SEM = 4.72; range = 4–19 tion for each prime notation with a paired t-test, and the V-function numbers out of 20 possible) of Braille numbers when displayed for coefficients with zero. 600 ms, and 74% (SEM = 3.81; range = 10–20 numbers out of 20 possible) of Braille numbers when displayed for 300 ms. 3. Results 3.5. Priming experiment 3.1. Braille reading speed tests Subjects performed at an accuracy of 99.8%. The responses were In all reading speed tests we report the number of correctly read recorded and analyzed offline, and additionally coded by the experi- numbers/letters/words in the allotted time. At the onset of the three- menter. Due to voice key failure we excluded 5.1% trials. RTs were week Braille course, the mean tactile single Braille number-reading adjusted for different verbal onset times for the different target num- speed among the participants was 11 numbers per minute (NPM) bers. In the pilot phase we measured onset times for naming target (SEM = 1.49; range = 3–28). The mean tactile single Braille letter- numbers: 3, 4, and 5 in 5 participants. Based on that procedure we reading speed among the participants was 15.9 letters per minute decided to add fixed 70 ms to all conditions within target number 5. (LPM) (SEM = 0.94; range = 7–26). The mean tactile Braille word- Subsequently, we calculated means and SDs individually for each par- reading speed among the participants was 4.9 words per minute (WPM) ticipant for each condition and excluded all RTs three standard devia- (SEM = 0.68; range = 1–14). The mean visual Braille word-reading tions above or below the mean (0.44%). speed among the participants was 19.6 words per minute (WPM) To control whether the participants recognized tactile primes, we (SEM = 1.47 range: 8–37). After the Braille course participants reached analyzed the accuracy of the performance in the catch trials, in which an averaged performance of 30.8 numbers per minute (NPM) participants were asked to additionally name the tactile prime that (SEM = 2.58 range: 6–49), 18.6 letters per minute (LPM) (SEM = 1.29 preceded the target. On average, participants correctly recognized range: 12–32), 6.3 words per minute (WPM) (SEM = 0.77 range: 1–14) 78.75% (SEM = 2.77, range 67–100%) of tactile primes during the in the tactile modality and 22.3 words per minute (WPM) (SEM = 1.43 experiment. Additionally, although in priming paradigms the subjects' range: 1–18) in the visual modality (Fig. 3A-C). conscious attention to primes is not necessary for the priming effect to To directly test for an increase in the Braille reading speed, we ran occur (e.g. Dehaene et al., 2001; Naccache & Dehaene, 2001), we tested paired t-tests between ‘before’ vs. ‘after’ course results from all tests in the pilot phase, whether the visual primes were visible for the par- described above. These analyses confirmed that the increase in Braille ticipants. We tested 10 independent participants, and all were able to reading speed was significant in all tests [tactile Braille numbers: t recognize the primes with 100% accuracy. Both Braille and number (19) = −8.598, p < .001; tactile Braille letters: t(19) = −3.008, words are considered symbolic notations and as such should not show p = .007; tactile Braille words: t(19) = 3.935, p < .001; visual Braille any interaction, however, to statistically test this assumption, we per- words: t(19) = −4.992, p < .001, Fig. 3A–C]. Thus, although the aim formed a repeated-measures ANOVA with prime notation (number

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Fig. 3. Braille number reading course. Sighted Braille readers (Bola et al., 2016), were given a three week Braille intensive number reading course. Results of Braille reading tests for tactile Braille reading (A–C) before and after the course. Graphs show the average number of Braille num- bers/letters/words (A–C) read per minute. After the Braille course participants read Braille digits three times faster than before the course (A). Significance levels: ***p < .001, **p<.01. Error bars represents S.E.M.

Fig. 4. Priming results. RTs for all prime-target combinations for the two different notations (A) Braille (B) number words. The error bars represent the SE following Cousineau-Morey corrections (Cousineau, 2005; Morey, 2008). words vs. Braille), prime and target value which revealed no significant (8,152) = 3.554; p = .001]. Together, these findings suggest that the main effect (all > 0.2). However, a significant interaction between primes had a significant impact on naming latencies. prime and target value [F(8,152) = 8.049; p < .001] provides the first To further analyze the impact of the numerical distance between evidence for a semantic priming effect. Importantly, significant inter- prime and target value, we separately computed a 3 (distance actions of prime notation with target [F(2,38) = 6.125; p = .005] and value) × 3 (target value) repeated-measures ANOVA on mean RTs for prime value [F(4,76) = 5.365; p = .001] were observed. No other in- both Braille and number words. As introduced above, we analyzed the teraction was observed. To follow up on these findings, we computed three targets with their identity primes (e.g. target 3 and prime 3), and separate repeated-measures ANOVAs for both prime notations. For nearest neighbor primes (e.g. target 5 and primes 4 and 6). For Braille Braille primes we observed a significant effect for prime [744, 739, 752, condition, this revealed a significant effect for distance [757, 729, and 747 and 758 ms for primes 2–6 respectively; F(4,76) = 2.780; 753 ms for distance −1, 0, and 1, respectively; F(2,38) = 12.211; p = .033] with no significant effect for target [758, 744, and 742 ms for p < .001] but no significant effect for target [751, 744, and 743 ms for targets 3–5, respectively; F(2,38) = 1.433; p = .251], but a significant target 3–5, respectively; F(2,38) = 0.424; p = .657], or interaction interaction between target and prime [F(8,152) = 4.275; p < .001]. between target and distance [F(4,76) = 1.424; p = .234]. We then An analogous repeated-measures ANOVA was then run on mean RTs for compared distances −1 and 1 for all targets [target 3: t(19) = 0.045, the number words condition. This revealed a significant effect for prime p = .965; target 4: t(19) = 1.732, p = .099; target 5: t(19) = −0.810, [739, 752, 740, 747 and 743 ms for primes 2–6, respectively; F p = .428]. The non-significant results make the assumption highly un- (4,76) = 3.811; p = .007], no significant effect for target [741, 752, likely that the activation strength was asymmetrical. and 739 ms for targets 3–5, respectively; F(2,38) = 0.706; p = .500], The corresponding analysis for number words revealed a significant but a significant interaction between target and prime [F effect for distance [747, 733, and 750 ms for distance −1to1,

6 ą K. R czy, et al. Acta Psychologica 202 (2020) 102960 respectively; F(2,38) = 6.933; p = .003] but no significant effect for and number words. This priming was best characterized by a V-shaped target [740, 754, and 736 ms for targets 3–5, respectively; F function in both notations. Further analyses revealed that the observed (2,38) = 1.200; p = .312] and significant interaction between target priming is due to identity priming rather than semantic priming. and distance [F(4,76) = 3.908; p = .006]. We then compared distances Participants were fastest at naming Arabic digits when the pri- −1 and 1 for all targets [target 3: t(19) = 0.760, p = .457; target 4: t me–target distance was zero (e.g. “three” to “3”), with a symmetrical (19) = −0.910, p = .374; target 5: t(19) = −1.012, p = .324]. The decrease of activation strength for neighboring numbers (e.g. “two” to non-significant results make the assumption highly unlikely that the “3” or “four” to “3”; Fig. 4) regardless of the prime notation. V-shaped activation strength was asymmetrical. and step-like priming functions are reported for symbolic (e.g. Arabic Since the seven levels of target–prime distance contain varying digits to Arabic digits; Koechlin et al., 1999; Naccache & Dehaene, numbers of observations (see Fig. 4), we opted to further investigate the 2001; Reynvoet et al., 2002) and non-symbolic numerical priming, re- impact of target–prime distance by means of a regression analysis. spectively (Roggeman et al., 2007; Van Opstal, Gevers, De Moor, & A comparison of the regression coefficients revealed a significant Verguts, 2008). Here, we found that the V-function predictor, contrary difference between the V-function and the step-function for Braille. V- to the step-like predictor, was the best predictor for Braille notation shape predictor — mean β = 6.72, MSE = 1.84. Step predictor — mean when performing both regression analyses (including all distances and β = −1.53, MSE = 1.94, t(19) = 2.827, p = .011. However, no sig- when restricting them to two). This suggests that Braille numbers al- nificant difference was found for the visual number words. V-shape lowed direct access to a numerical code rather than resulting in predictor — mean β = 1.35, MSE = 1.66. Step predictor — mean counting up to the ordinal position of the corresponding letter in the β = 2.35 MSE = 1.97, t(19) = −0.339, p = .739. The assumption of alphabet. collinearity was not violated (all distances: target predictor We did not observe any evidence for semantic priming beyond a VIF = 1.138, V-shape predictor VIF = 1.103. step-shape predictor target–prime distance of ± 1; this diverges from earlier results obtained VIF = 1.241). We also tested whether the V-function predictors differed by Roggeman et al. (2007). One major difference between our paradigm significantly from zero. These analysis showed a significant difference and the task used by Roggeman et al. (2007) is the symbolic priming for the V-function predictor when compared to zero for Braille notation notation. While Roggeman et al. (2007) observed semantic V-shaped [t(19) = 3.653; p = .002] but not for number words [t(19) = 0.814; priming with Arabic digit primes, we did not observe such a semantic p = .426]. We then removed data point target-prime 0 to further test priming using number word primes. This leads to an important question whether the V-shape curve was determined by identity priming or concerning the nature of the activated code. Did prime and/or target whether it additionally reflects distance-related priming and thus se- numbers in our task activate a semantic number code or did partici- mantic access (following Roggeman et al., 2007). A comparison of the pants engage in a direct conversion of the Arabic number () V-shape predictor with 0 revealed a non-significant difference for into a phoneme (identity priming)? In our results, we observed a strong Braille (mean β = −1.49, MSE = 2.15, t(19) = −0.691, p = .498, 2- effect of repetition priming but no strong evidence for an impact of tailed) indicating no priming beyond distance −1/1 and thus no se- numerical distance larger than one between prime and target, which mantic access; a significant difference for visual number words (mean would be typical for semantic code activation. Based on the Triple Code β = −4.18, MSE = 1.87, t(19) = −2.236, p = .038, 2-tailed) in- Model of number processing (Dehaene & Cohen, 1995), we propose that dicating an “inverse” semantic priming. While for Braille we observe an the mechanism responsible for priming effects in our paradigm is a identity priming and no evidence for semantic access, for number words direct grapheme–phoneme conversion. Under this mechanism, both there are two effects: an identity priming with an “inverse” semantic Braille numbers and number words directly activate a phonological priming. Since priming effects are particularly dependent on stimulus number code which, in turn, was accessed by the Arabic digit target timing, the observed “inverse” semantic priming might directly results (Fig. 1). from SOA (stimulus-onset asynchrony) used in our design. In line with The V-shape coding obtained in our paradigm is most likely driven our a priori predictions, we restricted regression analysis to distances by identity priming, and is thus different in some aspects from the V- −1 up to 1 (including zero distance) in order to keep the same tar- shaped coding described by Roggeman et al. (2007) for Arabic digit get–prime distance for each target used in the experiment. This re- primes and targets. In contrast to us, Roggeman et al. (2007) did ob- vealed a significant difference between the V-function and step-function serve an effect of numerical distance between prime and target; this is for both prime notations [Braille: V-shape predictor — mean β = 27.40, suggestive of semantic code activation for Arabic digit primes and MSE = 6.25; step predictor — mean β = −2.16, MSE = 2.44, t targets. This difference suggests that compared to Arabic digits, number (19) = 4.004, p = .001. Number words: V-shape predictor — mean words are less prone to automatically activating a semantic number β = 14.11, MSE = 4.24; step predictor — mean β = 1.35 MSE = 2.39, t code. (19) = 2.347, p = .030, Fig. 5C]. The assumption of collinearity was Surprisingly, the repetition priming was marginally stronger for not violated (target predictor VIF = 1.000, V-shape predictor Braille compared to number words. Assuming that the grapheme–- VIF = 1.333. step-shape predictor VIF = 1.333). The V-function pre- phoneme conversion is more automatized for number words, this dictor was the best predictor for both the Braille and number words finding may be explained by the procedural difference in our paradigm. notation. We subsequently ran t-tests to verify whether the V-function Since Braille reading in general is more effortful than word reading, we predictors would differ significantly from zero; they revealed a sig- presented Braille primes for 300 ms, while number words were pre- nificant difference for V-function predictors of both notations [Braille: t sented for 83 ms only. This difference may be reflected by a slightly (19) = 4.386, p < .001. Number words: t(19) = 3.327, p = .004]. more pronounced priming effect for Braille in our experiment. Taken together, these results provide quantitative evidence of the dif- The different timings for different conditions are inevitably parti- ference between the V-shape and step-like priming curves for these two cular to specific modalities of the primes: the tactile, and the visual. For prime notations, with a striking difference between the V-shape and the visual priming to occur, the stimuli have to be presented in a very step-like priming curves for Braille. The difference of the V-shape re- fast manner. Here, prior to the main experiment we established the gression coefficients between Braille and number words only margin- shortest interval possible at which subjects could recognize Braille ally failed to reach statistical significance [t(19) = 1.784, p = .090]. numbers. Then — by adjusting remaining intervals accordingly — we observed a cross-modal priming. In the visual priming paradigms the 4. Discussion participants are presented with the mask to avoid an afterimage — a phenomenon unique for the visual stimuli not the tactile ones. It is The current study revealed three main findings. First, we observed a therefore very unlikely that different intervals used in the two condi- significant impact of numerical primes in both prime notations, Braille tions could have had affected the main finding presented here, namely

7 ą K. R czy, et al. Acta Psychologica 202 (2020) 102960

Fig. 5. (A) Single subject data shows RTs for three prime-target distances (1,0,-1) for Braille prime notation. Panel (B) illustrates the regressors for V-shape and steplike. Panel (C) shows mean regression coefficients for the predictors describing step-like and V-shape priming functions as a function of prime notation (for Braille notation and for number words notation). The regression was run for each participant separately. Error bars denotes S.E.. the occurrence of the tactile-to-visual number priming. observed effects are most likely due to pre-activation of a phonological In our study, we tested sighted people who learned Braille numbers code and thus, they bypass the mental number line. In our study, we when they were already fluent in recognizing Arabic digits. Such cross- observed V-shape priming pattern for Braille to Arabic digits priming, modal number priming is in line with the notion of a generalized which may be taken as evidence for place coding of Braille digits. magnitude system (Krause et al., 2013; Walsh, 2003). We propose that However, we have not observed any semantic access. Therefore, we during Braille acquisition our participants mapped to presume that processing Braille digits can bypass the semantic activa- their internal number representation. This supports the view that the tion of the mental number line (i.e. they directly prime the target Arabic brain processes abstract magnitude information according to a shared digit), at least when the prime was identical with the target. code, independent of the modality, which further reveals a direct re- Additionally, since there was no semantic access for Braille digits, we lationship between tactile and abstract numerosities and the presence presume that the priming effect occurred on the phonological level, i.e. of a magnitude code shared by both modalities. activated a phonological representation mutual for Braille and Arabic In conclusion, based on our observation of cross-modal priming, digits. In other words, we assume that processing Braille number acti- best characterized as identity priming, we propose that tactile Braille vated a phonological representation of its corresponding numerosity numbers and number words are place coded. We presume that the which, in case of identical numbers, was shared by an Arabic number.

8 ą K. R czy, et al. Acta Psychologica 202 (2020) 102960

This facilitation effect on the phonological level resulted in the ob- Psychology: Human Perception and Performance, 16(3), 626. served identity priming effect. This further signifies that Braille digits Dehaene, S., Naccache, ., Cohen, L., Le Bihan, D., Mangin, J. F., Poline, J. B., & Rivière, D. (2001). Cerebral mechanisms of word masking and unconscious repetition and Arabic digits share a code that is phonological rather than se- priming. Nature Neuroscience, 4(7), 752. mantic. In light of our findings, the Triple Code within the Triple Code Dehaene, S., Spelke, E., Pinel, P., Stanescu, R., & Tsivkin, S. (1999). Sources of mathe- Model (Dehaene et al., 1999; Molko et al., 2003) becomes a Quadruple matical thinking: Behavioral and brain-imaging evidence. Science, 284(5416), 970–974. https://doi.org/10.1126/science.284.5416.970. Code, since we have to assume an additional tactile number code for Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Braille numbers, which might, or might not share some of its re- Cognitive Sciences, 8(7), 307–314. https://doi.org/10.1016/j.tics.2004.05.002. presentations with the visual and/or the phonological number code (see Hesselmann, G., Darcy, ., Sterzer, P., & Knops, A. (2015). Exploring the boundary ff fl Siuda-Krzywicka et al., 2016). conditions of unconscious numerical priming e ects with continuous ash suppres- sion. Consciousness and Cognition, 31,60–72. https://doi.org/10.1016/j.concog.2014. Finally, we wish to emphasize that the above conclusions are valid 10.009. for the particular population we studied. Our subjects were slow Hesselmann, G., & Knops, A. (2014). No conclusive evidence for numerical priming under – readers, with skills roughly equivalent to second grade children. One interocular suppression. Psychological Science, 25(11), 2116 2119. Hunziker, . . (2006). Im Auge des Lesers: foveale und periphere Wahrnehmung-vom has to consider the fact that priming is notoriously dependent on sti- Buchstabieren zur Lesefreude [The eye of the reader: Foveal and peripheral mulus timing, that stimulus timing was, by necessity, slow, and that the perception—From letter recognition to the joy of reading]. Zurich: Transmedia. subjects processing of Braille digits, while symbolic, was much less Kadosh, R. C., & Walsh, V. (2009). Numerical representation in the parietal lobes: Abstract or not abstract? Behavioral and Brain Sciences, 32(3–4), 313. https://doi.org/ practiced than their processing of Arabic digits. To our knowledge, our 10.1017/S0140525X09990938. subjects are the only group of dual tactile-visual readers described so Knops, A. (2017). Probing the neural correlates of number processing. The Neuroscientist, far, and it remains to be proven whether surpassing their skills is 23(3), 264–274. https://doi.org/10.1177/1073858416650153. 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F., Bruandet, M., Le Bihan, D., ... Dehaene, S. National Science Centre to M.S. We would like to thank all our parti- (2003). Functional and structural alterations of the intraparietal sulcus in a devel- – cipants for their effort and for participating in the study, Paweł Hańczur opmental dyscalculia of genetic origin. Neuron, 40(4), 847 858. Morey, R. D. (2008). Confidence intervals from normalized data: A correction to for programming the Braille Display and Jochen Laubrock for helpful Cousineau (2005). Tutorials in Quantitative Methods for Psychology, 4(2), 61–64. comments. We would like to acknowledge the Maria Grzegorzewska https://doi.org/10.20982/tqmp.04.2.p061. University in Warsaw for organizational help. We thank the Laboratory Naccache, L., & Dehaene, S. (2001). The priming method: Imaging unconscious repetition priming reveals an abstract representation of number in the parietal lobes. 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